$\lfloor \sqrt n+\sqrt {n+1}+\sqrt{n+2}+\sqrt{n+3}+\sqrt{n+4}\rfloor=?iso-8859-1?Q?=3D\lfloor\sqrt_{25n+49}\rfloor$_is_true=3F_=96_math.stack?=exchange.com

$\lfloor \sqrt n+\sqrt
{n+1}+\sqrt{n+2}+\sqrt{n+3}+\sqrt{n+4}\rfloor=\lfloor\sqrt
{25n+49}\rfloor$ is true? – math.stackexchange.com

I found the following relational expression by using computer: For any
natural number $n$, $$\lfloor \sqrt n+\sqrt
{n+1}+\sqrt{n+2}+\sqrt{n+3}+\sqrt{n+4}\rfloor=\lfloor\sqrt
{25n+49}\rfloor.$$ Note …